Home
Class 12
MATHS
Evaluate: int(4x+1)/(x^2+3x+2)\ dx...

Evaluate: `int(4x+1)/(x^2+3x+2)\ dx`

Text Solution

Verified by Experts

`I=int(4x+1)/(x^(2)+3x+2)dx`
`=int(2(2x+3)-5)/(x^(2)+3x+2)dx`
`=2int(2x+3)/(x^(2)+3x+2)dx-5int(1)/(x^(2)+3x+2)dx`
`=2log|x^(2)+3x+2|-5int(1)/(x^(2)+3x+(9//4)-(9//4)+2)dx`
`=2log|x^(2)+3x+2|-5int(1)/((x+3//2)^(2)-(1//2)^(2))dx`
`=2log|x^(2)+3x+2|-5(1)/(2(1//2))log|(x+(3)/(2)-(1)/(2))/(x+(3)/(2)+(1)/(2))|+C`
`=2log|x^(2)+3x+2|-5log|(x+1)/(x+2)|+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise EXAMPLE|18 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(x+1)/(x^2+4x+5)\ dx

Evaluate: int(x-1)/(4x^2-4x+3)\ dx

Evaluate: int(3-4x)/(2x^(2)-3x+1)dx

Evaluate: int(2x+1)/(x^2+x+3)dx

Evaluate: int(x-3)/(x^2+2x-4)\ dx

Evaluate: int(3x-1)/((x+2)^2)\ dx

Evaluate: int(3x)/(1+2x^4)dx

Evaluate: int_2^4x/(x^2+1)dx

int (x+1)/(2x^2+3x+4) dx

Evaluate: int(2x+1)/((x-2)(x-3))\ dx